Colorectal cancer (CRC) is the second leading cause of cancer death in the United States and is responsible for significant morbidity and mortality. A patient's five-year survival rate depend on the tumor stage at the time of diagnosis, and stage of the tumor plays a substantial role in decision-making regarding treatment. Thus, precise pre-treatment diagnostic evaluation and staging of colorectal cancer are important. In addition, angiogenesis plays an important role in the process of growth and metastasis in CRC and is reported as a useful prognostic marker, similar to many other carcinomas. Thus, in vivo quantification of the tumor angiogenesis rate holds promise in improving the management of CRC. Perfusion computed tomography (PCT) acquires high temporal resolution images, thus enabling evaluation of hemodynamic changes of tissue in vivo by modeling tracer kinetics. PCT has been reported to characterize tumor angiogenesis, and to be a more sensitive imaging biomarker for predicting of overall survival (OS) of CRC patients than conventional tumor staging. In clinical practice, however, the PCT protocol is a trade-off between high-temporal resolution and the total radiation dose required. Thus, the use of dynamic CT imaging derived from four temporal phases, which include pre-contrast, arterial, portal, and delayed phases, is highly desirable, because it is more readily available and yields substantially lower radiation exposure to the patients than that of PCT. However, low temporal resolution in four-phase dynamic CT presents several barriers in modeling tracer kinetics, primarily because of the lack of temporal enhancement information, which limits the ability to obtain reliable physiological information. We will thus develop a novel continuous-time modeling of tracer kinetics without any discretization of the enhancement curves. Such an approach will enable estimation of the time lag between onset time points of input and response enhancements as well as other kinetic parameters in four-phase dynamic CT. We hypothesize that the proposed tracer kinetic model can be an effective imaging biomarker for the risk stratification of recurrence of CRC and for prediction of OS. To explore these hypotheses, the specific aims of the proposed project are (1) Develop a novel single-input continuous-time tracer kinetic model without any discretization to fit temporal enhancement curves in four-phase dynamic CT of the colon, and (2) develop kinetic-model-based imaging biomarkers from four-phase dynamic CT and evaluate their performance in predicting clinical outcome in CRC patients. Successful development of a novel imaging biomarker based on four-phase dynamic CT holds high promise for the development of tailor-made optimal therapy without excessive radiation exposure to the patient.